Question

17. Which points satisfy the polynomial p(x) = x2 – X-6
A (-2,0) B (0,-6) C(3,-1) D(2,-4) E(-1,4) F(3,0)​

Answer 1

Answer:

$correct \: option \: \: is \: \: \: (a) \: \: \: ( - 2 \: \: \: \: 0).$

Step-by-step explanation:

${x}^{2} - x - 6 = {x}^{2} - 3 x+ 2x - 6 \\ \\ = x(x - 3) + 2(x - 3) \\ \\ = (x + 2)(x - 3) = 0 \\ \\ x = - 2 \: \: \: \: \: \: \: \: or \: \: \: \: \: x = 3 \\ \\ therefore \: \: \: \: p( - 2) = 4 - ( - 2) - 6 = 4 + 2 - 6 = 0 \\ \\ \\ and \: \: \: p(3) = 9 - 9 - 6 = - 6 \\ \\ \\ therefore \: \: \: ( - 2 \: \: \: \: \: \: 0) \: \: \: \: \: \: \: and \: \: \: \: \: \: (3 \: \: \: \: \: \: - 6) \\ \\ \\ therefore \: \: \: \: correct \: option \: \: is \: \: \: (a) \: \: \: ( - 2 \: \: \: \: 0).$